the Isle of Wight zoo is becoming, slowly, one of the best places for tigers (although the majority aren't yet enjoying new enclosures, but signs are hopeful)
http://www.zoobeat.com/38/isle-wight-zoo-esp-tigers-14693/
I generally view safari parks as having the best space for large cats, certainly longleat has fantastic lion and tiger accommodation.
Port Lympne have a good amur tiger enclosure, in the pine trees at the top of the hill, and good scrub/bush type enclosures at the bottom for some of the barbary lions, in that they can disappear into the bushes easily if they wish to escape the public view. They also have one of the best snow leopard enclosures I have seen. Open-topped, running down a steep hillside, with dense vegetation and mature trees, but also a rocky outcrop which they tend to use to look out over the hillside.
The most diverse 'collection' of large cats in the UK right now is at the Wildlife Heritage foundation in Smarden, Kent:
http://www.whf.org.uk/index.cfm
The site used to belong to Born free but now it is owned by Paradise Wildife Park. Currently it isn't open to the public except for 'experience days' etc..they have Amur, North Chinese, and Snow leopards, Cheetahs, Amur, Sumatran and 'bengal' tigers, as well as african lions. From footage I have seen, the enclosures are pretty average, it is quite an open site with little vegetation from what I can see.